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Problem 72

The combustion of one mole of liquid octane, $\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{6} \mathrm{CH}_{3}$ produces 5470 $\mathrm{kJ}$ of heat. Calculate how much heat is produced if 1.000 gallon of octane is combusted. See Exercise 3.68 for necessary information about octane.

$1.27 \times 10^{5} \mathrm{kJ}$

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## Video Transcript

So in this problem, we're as that on the compassion off. One mole off liquid oct in ah can produce five, four, seven zero killers Jule off hit. We have to calculate how much it is produced if one gallon off tiny's Col mustard. So first you have to find out the number ofthe malls off ock ten for one gallon, off walked in. And from there we can say that if one more off OCD and can produce this much it, then that moral fork then will produce that much heat. So first we have to convert one gallon, tow the militar, and from there using ah, using the density of Faulkner and we can find out the massive for Clint and from their mess, we can find the number of moles by just dividing the mass by the molar mass Now one gallon off Ogden or wanna get off any substances, Um, through seven eight, five point four million later. Now the density of OCD And is it zero pond seven or three, Grandpa are ml. That means, um, the mass off one gallon Ogden is equal to through seven eight five point four million later times zero point seven or three. Grandpa Ramo, which will give us a hand off two six six, one point one four gram Stockton. So this is the mass ofthe one gallon locked in. Now we have to divide this by the Moler massive Falken to get the number of mall so fucked in. So the number of malls for this much octane ese So six, six, one bland one for gram over the molar mass of oxygen, which is one hundred fourteen point toe trade. Crump, Armel. And this will give us a value off twenty three. Plant three zero mall. I said, this is the number of mole for one getting knocked. And now we have seen that one matloff octane can produce five four seven zero kilo Jule off it, that means twenty three points, three zero more octane will produce five four seven zero killer Jule times. Um, twenty three point three zero. And it could give us a fellow off one point two seven times tenderly bar five killers Soul. So one point two seven times and never fight. Still, a jewel heat will be perused from twenty three point three zero mall and our one gallon off walked in